The problem asks how much money will be left after seven years if a man invests Tk. 10,000, withdraws Tk. 1500 at the end of each year starting at the end of the first year, and the money is invested at 4% per annum.

1. Problem Description

The problem asks how much money will be left after seven years if a man invests Tk. 10,000, withdraws Tk. 1500 at the end of each year starting at the end of the first year, and the money is invested at 4% per annum.

2. Solution Steps

We need to calculate the future value of the initial investment and subtract the future value of the withdrawals.

The future value of the initial investment after 7 years is given by:

$FV = PV (1 + r)^n$

where $PV$ is the present value (initial investment), $r$ is the interest rate, and $n$ is the number of years.

$FV = 10000 (1 + 0.04)^7 = 10000 (1.04)^7 = 10000 \times 1.31593177923808 = 13159.32$

The withdrawals are an ordinary annuity. The future value of an ordinary annuity is given by:

$FV = PMT \times \frac{(1 + r)^n - 1}{r}$

where $PMT$ is the payment amount, $r$ is the interest rate, and $n$ is the number of years.

$FV = 1500 \times \frac{(1.04)^7 - 1}{0.04} = 1500 \times \frac{1.31593177923808 - 1}{0.04} = 1500 \times \frac{0.31593177923808}{0.04} = 1500 \times 7.898294480952 = 11847.44$

The amount left after seven years is the future value of the initial investment minus the future value of the withdrawals:

$13159.32 - 11847.44 = 1311.88$

3. Final Answer

Tk. 1311.88 will be left after seven years.